In known hydraulic machines comprising a rotor in a housing, in particular pumps, the rotor must have a relatively large running clearance with respect to the associated housing parts so that no disadvantages occur due to different thermal expansion of the rotor and housing. For example, on starting a cold pump the rotor temperature T.sub.R (measured in the region of the rotor width) and the temperature T.sub.G of the housing in the region of the rotor (e.g. the temperature T.sub.G of the housing center part) exhibit a very different variation as a function of time. As a result, at a certain instant a very large temperature difference T.sub.R -T.sub.G results so that due to thermal expansion a reduction of the axial clearance between the rotor and the associated planar faces of the housing occurs. To prevent seizure of the rotor at this instant the axial clearance must therefore be made correspondingly large which leads to an increase in the volumetric losses and a reduction in efficiency.